The Binomial Theorem. Binomial is a word used in algebra that roughly means “two things added together.” The binomial theorem refers to the pattern of coefficients ...

Binomial Theorem. Binomial theorem is used for the expansion of any positive integral power of binomial expression. In the expansion of (a + b) n, the general term is denoted as T r + 1 ...

The binomial theorem states that for all real numbers x and y for all positive integers n. Note: There are (n + 1) terms in the above expansion of (x+y) n.

A modern proof of the theorem occupies about one paragraph. A far more powerful version, the strong law of large numbers, was proved by Émile Borel in 1909. But all modern extensions spring from ...